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# For each positive integer,the quantity [size=150]S[/size]n i

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Intern
Joined: 13 May 2013
Posts: 20
For each positive integer,the quantity [size=150]S[/size]n i  [#permalink]

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21 Aug 2013, 23:08
2
00:00

Difficulty:

55% (hard)

Question Stats:

69% (01:53) correct 31% (01:38) wrong based on 36 sessions

### HideShow timer Statistics

For each positive integer,the quantity Sn is defined such that Sn+2=(Sn)^2 - S(n+1).in addition ,S2=1.then which of the following must be true.

a) S4 +S3 +1=0
b) (S1)^2 +S4 +2=0
c) if S1=-1 then S4 is also equal to -1.
d) if S4 =-7 then S1=-2.
e) if S1 =-3 then S4= -7
Intern
Joined: 25 Jul 2012
Posts: 10
Concentration: Finance, Entrepreneurship
GPA: 3.56
Re: For each positive integer,the quantity [size=150]S[/size]n i  [#permalink]

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22 Aug 2013, 02:05
Since all the answers include S4, let's start from there.

S4=S2^2-S3

S3=S1^2-S2

Substituting S3 into the first equation we get:

S4=S2^2-(S1^2-S2)

Since S2=1

S4=1-(S1^2-1)
S4=2-S1^2

We need S1^2 in order to calculate S4.

E) provides S1 and from there we can calculate S4:

S4=2-(-3)^2
S4=-7

Correct.

As a side note, I would be very careful with answers in the form "if S4=x then S1=y" (such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer.

For example:

If S4=-7 then S1=3 :

if we substitute S4 with - 7 we get:

-7=2-S1^2
S1^2=9

now S1 can be +/-3 !!

That being said, I highly doubt GMAT would test something like this.

Cheers,
Non-Human User
Joined: 09 Sep 2013
Posts: 9836
Re: For each positive integer,the quantity [size=150]S[/size]n i  [#permalink]

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09 Oct 2018, 18:05
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Re: For each positive integer,the quantity [size=150]S[/size]n i   [#permalink] 09 Oct 2018, 18:05
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